Metamath Proof Explorer


Theorem nnnn0i

Description: A positive integer is a nonnegative integer. (Contributed by NM, 20-Jun-2005)

Ref Expression
Hypothesis nnnn0i.1 ⊢ N ∈ ℕ
Assertion nnnn0i ⊢ N ∈ ℕ 0

Proof

Step Hyp Ref Expression
1 nnnn0i.1 ⊢ N ∈ ℕ
2 nnnn0 ⊢ N ∈ ℕ → N ∈ ℕ 0
3 1 2 ax-mp ⊢ N ∈ ℕ 0